You
could buy the full sized model then just switch the stock out for an 870 youth sized stock.
Like this...kind of expensive, but it's a really nice stock -
Hogue OverMolded Stock Remington 870 with 12" Length of Pull Rubber Black - MidwayUSA
If you did decide to go with that stock I'd check with Hogue to make sure it would fit the 20 gauge model, because I heard it uses a smaller sized action than the 12 gauge.